Circuits including a given set of vertices

Let G = (V, E) be a digraph of order n, satisfying Woodall's condition ? x, y ∈ V, if (x, y) ? E, then d⁺(x) + d^?(y) ≥ n. Let S be a subset of V of cardinality s. Then there exists a circuit including S and of length at most Min(n, 2s). In the case of oriented graphs we obtain the same result under the weaker condition d⁺(x) + d^?(y) ≥ n – 2 (which implies hamiltonism).